Efficient Treatment of Gyroscopic Bodies in the Recursive Solution of Multibody Dynamics Equations

This paper presents an efficient treatment of gyroscopic bodies in the recursive solution of the dynamics of an $N$-body system. The bodies of interest include the reaction wheels in satellites, wheels on a car, and flywheels in machines. More specifically, these bodies have diagonal inertia tensors. They spin about one of its principal axes, with the moment of inertia along the transverse axes identical. Their center of mass lies on the spin axis. Current recursive solution methods treat these bodies identically as any other body in the system. The proposition here is that a body with gyroscopic children can be collectively treated as a composite body in the recursive solution process. It will be shown that this proposition improves the recursive solution speed to the $order(N−m)$ where $m$ is the number of gyroscopic bodies in the system. A satellite with three reaction wheels is used to illustrate the proposition.